- #1
HallsofIvy said:Or:
[tex]\frac{x^2}{x^2+ a}= \frac{x^2+ a- a}{x^2+ a}= \frac{x^2+ a}{x^2+ a}-\frac{a}{x^2+ a}= 1- \frac{a}{x^2+a}[/tex]
hokhani said:how can i write equations ?
This is so beautiful!HallsofIvy said:Or:
[tex]\frac{x^2}{x^2+ a}= \frac{x^2+ a- a}{x^2+ a}= \frac{x^2+ a}{x^2+ a}-\frac{a}{x^2+ a}= 1- \frac{a}{x^2+a}[/tex]
The boundaries of an integral are typically given in the problem or can be determined by the limits of the function being integrated. Look for any given values for x or y, or consider the domain and range of the function to determine the boundaries.
A definite integral has specific boundaries and will give a numerical value, while an indefinite integral has no boundaries and will give a general equation. Definite integrals are used to find the area under a curve, while indefinite integrals are used to find the original function.
The appropriate integration technique depends on the form of the function being integrated. Some common techniques include substitution, integration by parts, and trigonometric substitution. It is important to identify the form of the function and choose the appropriate technique accordingly.
Some common mistakes when calculating integrals include forgetting to include the constant of integration, errors in algebraic manipulation, and forgetting to change the limits of integration when using substitution. It is important to carefully check all steps and double check the final answer.
Yes, many scientific and graphing calculators have built-in integration functions that can quickly solve integrals. However, it is important to still understand the process and be able to solve integrals by hand to check for accuracy. Additionally, not all integrals can be solved using a calculator.